Problem

Source: 2021 Saudi Arabia IMO TST p2 (1.2)

Tags: perfect number, power of 2, phi function, number theory



Find all positive integers $n$, such that $n$ is a perfect number and $\varphi (n)$ is power of $2$. Note:a positive integer $n$, is called perfect if the sum of all its positive divisors is equal to $2n$.